Single-particle and collective modes of weakly interacting condensed Bose gases within a conserving gapless mean-field theory

Takafumi Kita

Yoshiyuki Kondo, Takafumi Kita

We develop a mean-field theory for Bose-Einstein condensation of spin-1 atoms with internal degrees of freedom. It is applicable to nonuniform systems at finite temperatures with a plausible feature of satisfying the Hugenholtz-Pines theorem and various conservation laws simultaneously. Using it, we clarify thermodynamic properties and the excitation spectra of a uniform gas. The condensate is confirmed to remain in the same internal state from T=0 up to $T_{c}$ for both antiferromagnetic and ferromagnetic interactions. The excitation spectra of the antiferromagnetic (ferromagnetic) interaction are found to have only a single gapless mode, contrary to the prediction of the Bogoliubov theory where three (two) of them are gapless. We present a detailed discussion on those single-particle excitations in connection with the collective excitations.

Lushuai Cao, Robert Schmitz, Sven Kr onke +1 more

Phan Thành Nam, Robert Seiringer

Yasunari Kurita, Michikazu Kobayashi, Hideki Ishihara +1 more

We formulate particle-creation phenomena in Bose-Einstein condensates in terms of conserving gapless mean-field theory for weakly interacting Bose gases. The particle-creation spectrum is calculated by rediagonalizing the Bogoliubov--de Gennes (BdG) Hamiltonian in mean-field theory. The conservation implies that quasiparticle creation is accompanied by quantum back reaction to the condensates. Particle creation in this mean-field theory is found to be equivalent to that in quantum field theory (QFT) in curved space-time. An expression is obtained for an effective metric affected by quantum back reaction. The formula for the particle-creation spectrum obtained in terms of QFT in curved space-time is shown to be the same as that given by rediagonalizing the BdG Hamiltonian.

Takafumi Kita

This paper presents a conserving gapless mean-field theory for weakly interacting Bose gases. We first construct a mean-field Luttinger-Ward thermodynamic functional in terms of the condensate wave function $Ψ$ and the Nambu Green's function $\hat{G}$ for the quasiparticle field. Imposing its stationarity respect to $Ψ$ and $\hat{G}$ yields a set of equations to determine the equilibrium for general non-uniform systems. They have a plausible property of satisfying the Hugenholtz-Pines theorem to provide a gapless excitation spectrum. Also, the corresponding dynamical equations of motion obey various conservation laws. Thus, the present mean-field theory shares two important properties with the exact theory: ``conserving'' and ``gapless.'' The theory is then applied to a homogeneous weakly interacting Bose gas with s-wave scattering length $a$ and particle mass $m$ to clarify its basic thermodynamic properties under two complementary conditions of constant density $n$ and constant pressure $p$. The superfluid transition is predicted to be first-order because of the non-analytic nature of the order-parameter expansion near $T_{c}$ inherent in Bose systems, i.e., the Landau-Ginzburg expansion is not possible here. The transition temperature $T_{c}$ shows quite a different interaction dependence between the $n$-fixed and $p$-fixed cases. In the former case $T_{c}$ increases from the ideal gas value $T_{0}$ as $T_{c}/T_{0}= 1+ 2.33 an^{1/3}$, whereas it decreases in the latter as $T_{c}/T_{0}= 1- 3.84a(mp/2π\hbar^{2})^{1/5}$. Temperature dependences of basic thermodynamic quantities are clarified explicitly.